What types of cassegrain telescopes are there?
The Wikipedia article makes a decent resource useful to enable further research; the list, though I'm no authority on whether it is exhaustive or not (and I would think not), starts with the 'classic' cassegrain and then a few adaptations (Ritchey–Chrétien, Dall–Kirkham), to catadioptric assemblies (Schmidt, Maksutov.)
In the case of the non-catadioptrics types, each of these seem simply to tweak shape and / or tilt of mirrors, whereas the catadioptrics combine technologies - neither assuming something different, but each fit for purpose (though, for whatever flaws some might seem to correct in the original design, regression of sorts can become apparent in the features (as mentioned in the linked article regarding the 'off-axis configurations'.)
What type are most professional telescopes?
Even with just these few, we see utilisation of various types of telescope - the variety itself is the benefit of the game here, the availability of such allowing us to select based on the MO; for instance, if all telescopes were X-ray types then we'd be missing out, yet that's no reason not to have one or some of that type.
Surely cost is going to differ from one to the other, but in building to such scales and purposes I'm not so sure this would be a deciding factor, and so don't think we can huge bring economical benefits into it. Lastly, harking back to manufacture: I do believe that one benefit of the cassegrain type telescope over that of the Newtonian and refractor is that the cassegrain can be constructed more compactly while retaining aperture. In turn, we can infer that this ought to make them cheaper.